This workbook was created using the “dataexpks” template:

https://github.com/DublinLearningGroup/dataexpks

1 Introduction

This workbook performs the basic data exploration of the dataset.

level_exclusion_threshold <- 100

cat_level_count <- 40
hist_bins_count <- 50

2 Load Data

First we load the dataset.

rawdata_tbl <- read_rds("data/modelling2_data_tbl.rds") %>% select(-sev_data)

rawdata_tbl %>% glimpse()
## Rows: 678,019
## Columns: 13
## $ pol_id      <chr> "1", "3", "5", "10", "11", "13", "15", "17", "18", "21", …
## $ exposure    <dbl> 0.10, 0.77, 0.75, 0.09, 0.84, 0.52, 0.45, 0.27, 0.71, 0.1…
## $ veh_power   <chr> "5", "5", "6", "7", "7", "6", "6", "7", "7", "7", "7", "7…
## $ veh_age     <int> 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 9, 0, 2, 2, 2, …
## $ driv_age    <int> 55, 55, 52, 46, 46, 38, 38, 33, 33, 41, 41, 56, 27, 27, 2…
## $ bonus_malus <int> 50, 50, 50, 50, 50, 50, 50, 68, 68, 50, 50, 50, 90, 90, 1…
## $ veh_brand   <fct> B12, B12, B12, B12, B12, B12, B12, B12, B12, B12, B12, B1…
## $ veh_gas     <chr> "Regular", "Regular", "Diesel", "Diesel", "Diesel", "Regu…
## $ area        <fct> D, D, B, B, B, E, E, C, C, B, B, C, D, D, E, F, A, A, A, …
## $ density     <int> 1217, 1217, 54, 76, 76, 3003, 3003, 137, 137, 60, 60, 173…
## $ region      <fct> Rhone-Alpes, Rhone-Alpes, Picardie, Aquitaine, Aquitaine,…
## $ claim_total <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ claim_count <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …

2.1 Perform Quick Data Cleaning

cleaned_names <- rawdata_tbl %>% names()

data_tbl <- rawdata_tbl %>% set_colnames(cleaned_names)

data_tbl %>% glimpse()
## Rows: 678,019
## Columns: 13
## $ pol_id      <chr> "1", "3", "5", "10", "11", "13", "15", "17", "18", "21", …
## $ exposure    <dbl> 0.10, 0.77, 0.75, 0.09, 0.84, 0.52, 0.45, 0.27, 0.71, 0.1…
## $ veh_power   <chr> "5", "5", "6", "7", "7", "6", "6", "7", "7", "7", "7", "7…
## $ veh_age     <int> 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 9, 0, 2, 2, 2, …
## $ driv_age    <int> 55, 55, 52, 46, 46, 38, 38, 33, 33, 41, 41, 56, 27, 27, 2…
## $ bonus_malus <int> 50, 50, 50, 50, 50, 50, 50, 68, 68, 50, 50, 50, 90, 90, 1…
## $ veh_brand   <fct> B12, B12, B12, B12, B12, B12, B12, B12, B12, B12, B12, B1…
## $ veh_gas     <chr> "Regular", "Regular", "Diesel", "Diesel", "Diesel", "Regu…
## $ area        <fct> D, D, B, B, B, E, E, C, C, B, B, C, D, D, E, F, A, A, A, …
## $ density     <int> 1217, 1217, 54, 76, 76, 3003, 3003, 137, 137, 60, 60, 173…
## $ region      <fct> Rhone-Alpes, Rhone-Alpes, Picardie, Aquitaine, Aquitaine,…
## $ claim_total <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ claim_count <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …

2.2 Create Derived Variables

We now create derived features useful for modelling. These values are new variables calculated from existing variables in the data.

## Rows: 678,019
## Columns: 13
## $ pol_id      <chr> "1", "3", "5", "10", "11", "13", "15", "17", "18", "21", …
## $ exposure    <dbl> 0.10, 0.77, 0.75, 0.09, 0.84, 0.52, 0.45, 0.27, 0.71, 0.1…
## $ veh_power   <chr> "5", "5", "6", "7", "7", "6", "6", "7", "7", "7", "7", "7…
## $ veh_age     <int> 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 9, 0, 2, 2, 2, …
## $ driv_age    <int> 55, 55, 52, 46, 46, 38, 38, 33, 33, 41, 41, 56, 27, 27, 2…
## $ bonus_malus <int> 50, 50, 50, 50, 50, 50, 50, 68, 68, 50, 50, 50, 90, 90, 1…
## $ veh_brand   <fct> B12, B12, B12, B12, B12, B12, B12, B12, B12, B12, B12, B1…
## $ veh_gas     <chr> "Regular", "Regular", "Diesel", "Diesel", "Diesel", "Regu…
## $ area        <fct> D, D, B, B, B, E, E, C, C, B, B, C, D, D, E, F, A, A, A, …
## $ density     <int> 1217, 1217, 54, 76, 76, 3003, 3003, 137, 137, 60, 60, 173…
## $ region      <fct> Rhone-Alpes, Rhone-Alpes, Picardie, Aquitaine, Aquitaine,…
## $ claim_total <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ claim_count <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …

2.3 Check Missing Values

Before we do anything with the data, we first check for missing values in the dataset. In some cases, missing data is coded by a special character rather than as a blank, so we first correct for this.

### _TEMPLATE_
### ADD CODE TO CORRECT FOR DATA ENCODING HERE

With missing data properly encoded, we now visualise the missing data in a number of different ways.

2.3.1 Univariate Missing Data

We first examine a simple univariate count of all the missing data:

row_count <- data_tbl %>% nrow()

missing_univariate_tbl <- data_tbl %>%
  summarise_all(list(~sum(are_na(.)))) %>%
  gather("variable", "missing_count") %>%
  mutate(missing_prop = missing_count / row_count)

ggplot(missing_univariate_tbl) +
  geom_bar(aes(x = fct_reorder(variable, -missing_prop),
               weight = missing_prop)) +
  xlab("Variable") +
  ylab("Missing Value Proportion") +
  theme(axis.text.x = element_text(angle = 90))

We remove all variables where all of the entries are missing

remove_vars <- missing_univariate_tbl %>%
  filter(missing_count == row_count) %>%
  pull(variable)

lessmiss_data_tbl <- data_tbl %>%
  select(-one_of(remove_vars))

With these columns removed, we repeat the exercise.

missing_univariate_tbl <- lessmiss_data_tbl %>%
  summarise_all(list(~sum(are_na(.)))) %>%
  gather("variable", "missing_count") %>%
  mutate(missing_prop = missing_count / row_count)

ggplot(missing_univariate_tbl) +
  geom_bar(aes(x = fct_reorder(variable, -missing_prop),
               weight = missing_prop)) +
  xlab("Variable") +
  ylab("Missing Value Proportion") +
  theme(axis.text.x = element_text(angle = 90))

To reduce the scale of this plot, we look at the top twenty missing data counts.

missing_univariate_top_tbl <- missing_univariate_tbl %>%
  arrange(desc(missing_count)) %>%
  top_n(n = 50, wt = missing_count)

ggplot(missing_univariate_top_tbl) +
  geom_bar(aes(x = fct_reorder(variable, -missing_prop),
               weight = missing_prop)) +
  xlab("Variable") +
  ylab("Missing Value Proportion") +
  theme(axis.text.x = element_text(angle = 90))

2.3.2 Multivariate Missing Data

It is useful to get an idea of what combinations of variables tend to have variables with missing values simultaneously, so to construct a visualisation for this we create a count of all the times given combinations of variables have missing values, producing a heat map for these combination counts.

row_count <- rawdata_tbl %>% nrow()

count_nas <- ~ .x %>% are_na() %>% vec_cast(integer())

missing_plot_tbl <- rawdata_tbl %>%
  mutate_all(count_nas) %>%
  mutate(label = pmap_chr(., str_c)) %>%
  group_by(label) %>%
  summarise_all(list(sum)) %>%
  arrange(desc(label)) %>%
  select(-label) %>%
  mutate(label_count = pmap_int(., pmax)) %>%
  gather("col", "count", -label_count) %>%
  mutate(miss_prop   = count / row_count,
         group_label = sprintf("%6.4f", round(label_count / row_count, 4))
        )

ggplot(missing_plot_tbl) +
  geom_tile(aes(x = col, y = group_label, fill = miss_prop), height = 0.8) +
  scale_fill_continuous() +
  scale_x_discrete(position = "top") +
  xlab("Variable") +
  ylab("Missing Value Proportion") +
  theme(axis.text.x = element_text(angle = 90))

This visualisation takes a little explaining.

Each row represents a combination of variables with simultaneous missing values. For each row in the graphic, the coloured entries show which particular variables are missing in that combination. The proportion of rows with that combination is displayed in both the label for the row and the colouring for the cells in the row.

2.4 Inspect High-level-count Categorical Variables

With the raw data loaded up we now remove obvious unique or near-unique variables that are not amenable to basic exploration and plotting.

coltype_lst <- create_coltype_list(data_tbl)

count_levels <- ~ .x %>% unique() %>% length()

catvar_valuecount_tbl <- data_tbl %>%
  summarise_at(coltype_lst$split$discrete, count_levels) %>%
  gather("var_name", "level_count") %>%
  arrange(-level_count)

print(catvar_valuecount_tbl)
## # A tibble: 6 x 2
##   var_name  level_count
##   <chr>           <int>
## 1 pol_id         678019
## 2 region             22
## 3 veh_power          13
## 4 veh_brand          12
## 5 area                7
## 6 veh_gas             3
row_count <- nrow(data_tbl)

cat(str_c("Dataset has ", row_count, " rows\n"))
## Dataset has 678019 rows

Now that we a table of the counts of all the categorical variables we can automatically exclude unique variables from the exploration, as the level count will match the row count.

unique_vars <- catvar_valuecount_tbl %>%
  filter(level_count == row_count) %>%
  pull(var_name)

print(unique_vars)
## [1] "pol_id"
explore_data_tbl <- data_tbl %>%
  select(-one_of(unique_vars))

Having removed the unique identifier variables from the dataset, we may also wish to exclude categoricals with high level counts also, so we create a vector of those variable names.

highcount_vars <- catvar_valuecount_tbl %>%
  filter(level_count >= level_exclusion_threshold,
         level_count < row_count) %>%
  pull(var_name)

cat(str_c(highcount_vars, collapse = ", "))

We now can continue doing some basic exploration of the data. We may also choose to remove some extra columns from the dataset.

### You may want to comment out these next few lines to customise which
### categoricals are kept in the exploration.
drop_vars <- c(highcount_vars)

if (length(drop_vars) > 0) {
  explore_data_tbl <- explore_data_tbl %>%
      select(-one_of(drop_vars))

  cat(str_c(drop_vars, collapse = ", "))
}

3 Univariate Data Exploration

Now that we have loaded the data we can prepare it for some basic data exploration. We first exclude the variables that are unique identifiers or similar, and tehen split the remaining variables out into various categories to help with the systematic data exploration.

coltype_lst <- create_coltype_list(explore_data_tbl)

print(coltype_lst)
## $split
## $split$continuous
## [1] "exposure"    "veh_age"     "driv_age"    "bonus_malus" "density"    
## [6] "claim_total" "claim_count"
## 
## $split$discrete
## [1] "veh_power" "veh_brand" "veh_gas"   "area"      "region"   
## 
## 
## $columns
##     exposure    veh_power      veh_age     driv_age  bonus_malus    veh_brand 
## "continuous"   "discrete" "continuous" "continuous" "continuous"   "discrete" 
##      veh_gas         area      density       region  claim_total  claim_count 
##   "discrete"   "discrete" "continuous"   "discrete" "continuous" "continuous"

3.1 Logical Variables

Logical variables only take two values: TRUE or FALSE. It is useful to see missing data as well though, so we also plot the count of those.

logical_vars <- coltype_lst$split$logical %>% sort()

for (plot_varname in logical_vars) {
  cat("--\n")
  cat(str_c(plot_varname, "\n"))

  na_count <- explore_data_tbl %>% pull(!! plot_varname) %>% are_na() %>% sum()

  explore_plot <- ggplot(explore_data_tbl) +
    geom_bar(aes(x = !! sym(plot_varname))) +
    xlab(plot_varname) +
    ylab("Count") +
    scale_y_continuous(labels = label_comma()) +
    ggtitle(str_c("Barplot of Counts for Variable: ", plot_varname,
                  " (", na_count, " missing values)")) +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5))

  plot(explore_plot)
}

3.2 Numeric Variables

Numeric variables are usually continuous in nature, though we also have integer data.

numeric_vars <- coltype_lst$split$continuous %>% sort()

for (plot_varname in numeric_vars) {
  cat("--\n")
  cat(str_c(plot_varname, "\n"))

  plot_var <- explore_data_tbl %>% pull(!! plot_varname)
  na_count <- plot_var %>% are_na() %>% sum()

  plot_var %>% summary %>% print

  explore_plot <- ggplot(explore_data_tbl) +
    geom_histogram(aes(x = !! sym(plot_varname)),
                   bins = hist_bins_count) +
    geom_vline(xintercept = mean(plot_var, na.rm = TRUE),
               colour = "red",   size = 1.5) +
    geom_vline(xintercept = median(plot_var, na.rm = TRUE),
               colour = "green", size = 1.5) +
    xlab(plot_varname) +
    ylab("Count") +
    scale_y_continuous(labels = label_comma()) +
    ggtitle(str_c("Histogram Plot for Variable: ", plot_varname,
                  " (", na_count, " missing values)"),
            subtitle = "(red line is mean, green line is median)")

  explore_std_plot <- explore_plot + scale_x_continuous(labels = label_comma())
  explore_log_plot <- explore_plot + scale_x_log10     (labels = label_comma())

  plot_grid(explore_std_plot,
            explore_log_plot, nrow = 2) %>% print()
}
## --
## bonus_malus
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   50.00   50.00   50.00   59.76   64.00  230.00       6

## --
## claim_count
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##  0.00000  0.00000  0.00000  0.03929  0.00000 66.00000

## --
## claim_total
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##       1     750    1172    2433    1346 4075401  653069

## --
## density
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##       1      92     393    1792    1658   27000       6

## --
## driv_age
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    18.0    34.0    44.0    45.5    55.0   100.0       6

## --
## exposure
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
## 0.002732 0.180000 0.490000 0.528750 0.990000 2.010000        6

## --
## veh_age
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   2.000   6.000   7.044  11.000 100.000       6

3.3 Categorical Variables

Categorical variables only have values from a limited, and usually fixed, number of possible values

categorical_vars <- coltype_lst$split$discrete %>% sort()

for (plot_varname in categorical_vars) {
  cat("--\n")
  cat(str_c(plot_varname, "\n"))

  na_count <- explore_data_tbl %>% pull(!! plot_varname) %>% are_na() %>% sum()

  plot_tbl <- explore_data_tbl %>%
    pull(!! plot_varname) %>%
    fct_lump(n = cat_level_count) %>%
    fct_count() %>%
    mutate(f = fct_relabel(f, str_trunc, width = 15))

  explore_plot <- ggplot(plot_tbl) +
    geom_bar(aes(x = fct_reorder(f, -n), weight = n)) +
    xlab(plot_varname) +
    ylab("Count") +
    scale_y_continuous(labels = label_comma()) +
    ggtitle(str_c("Barplot of Counts for Variable: ", plot_varname,
                  " (", na_count, " missing values)")) +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5))

  plot(explore_plot)
}
## --
## area

## --
## region

## --
## veh_brand

## --
## veh_gas

## --
## veh_power

3.4 Date/Time Variables

Date/Time variables represent calendar or time-based data should as time of the day, a date, or a timestamp.

datetime_vars <- coltype_lst$split$datetime %>% sort()

for (plot_varname in datetime_vars) {
  cat("--\n")
  cat(str_c(plot_varname, "\n"))

  plot_var <- explore_data_tbl %>% pull(!! plot_varname)
  na_count <- plot_var %>% are_na() %>% sum()

  plot_var %>% summary() %>% print()

  explore_plot <- ggplot(explore_data_tbl) +
    geom_histogram(aes(x = !! sym(plot_varname)),
                   bins = hist_bins_count) +
    xlab(plot_varname) +
    ylab("Count") +
    scale_y_continuous(labels = label_comma()) +
    ggtitle(str_c("Barplot of Dates/Times in Variable: ", plot_varname,
                  " (", na_count, " missing values)"))

  plot(explore_plot)
}

4 Bivariate Data Exploration

We now move on to looking at bivariate plots of the data set.

4.1 Facet Plots on Variables

A natural way to explore relationships in data is to create univariate visualisations facetted by a categorical value.

facet_varname <- "region"

facet_count_max <- 3

4.1.1 Logical Variables

For logical variables we facet on barplots of the levels, comparing TRUE, FALSE and missing data.

logical_vars <- logical_vars[!logical_vars %in% facet_varname] %>% sort()


for (plot_varname in logical_vars) {
  cat("--\n")
  cat(str_c(plot_varname, "\n"))

  plot_tbl <- data_tbl %>% filter(!are_na(!! plot_varname))

  explore_plot <- ggplot(plot_tbl) +
    geom_bar(aes(x = !! sym(plot_varname))) +
    facet_wrap(facet_varname, scales = "free") +
    xlab(plot_varname) +
    ylab("Count") +
    scale_y_continuous(labels = label_comma()) +
    ggtitle(str_c(facet_varname, "-Faceted Barplots for Variable: ",
                  plot_varname)) +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5))

  plot(explore_plot)
}

4.1.2 Numeric Variables

For numeric variables, we facet on histograms of the data.

for (plot_varname in numeric_vars) {
  cat("--\n")
  cat(str_c(plot_varname, "\n"))

  plot_tbl <- data_tbl %>% filter(!are_na(!! plot_varname))

  explore_plot <- ggplot(plot_tbl) +
    geom_histogram(aes(x = !! sym(plot_varname)),
                   bins = hist_bins_count) +
    facet_wrap(facet_varname, scales = "free") +
    xlab(plot_varname) +
    ylab("Count") +
    scale_y_continuous(labels = label_comma()) +
    ggtitle(str_c(facet_varname, "-Faceted Histogram for Variable: ",
                  plot_varname)) +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5))

  print(explore_plot + scale_x_continuous(labels = label_comma()))
  print(explore_plot + scale_x_log10     (labels = label_comma()))
}
## --
## bonus_malus

## --
## claim_count

## --
## claim_total

## --
## density

## --
## driv_age

## --
## exposure

## --
## veh_age

4.1.3 Categorical Variables

We treat categorical variables like logical variables, faceting the barplots of the different levels of the data.

categorical_vars <- categorical_vars[!categorical_vars %in% facet_varname] %>% sort()

for (plot_varname in categorical_vars) {
  cat("--\n")
  cat(str_c(plot_varname, "\n"))

  plot_tbl <- data_tbl %>%
    filter(!are_na(!! plot_varname)) %>%
    mutate(
      varname_trunc = fct_relabel(!! sym(plot_varname), str_trunc, width = 10)
      )

  explore_plot <- ggplot(plot_tbl) +
    geom_bar(aes(x = varname_trunc)) +
    facet_wrap(facet_varname, scales = "free") +
    xlab(plot_varname) +
    ylab("Count") +
    scale_y_continuous(labels = label_comma()) +
    ggtitle(str_c(facet_varname, "-Faceted Histogram for Variable: ",
                  plot_varname)) +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5))

  plot(explore_plot)
}
## --
## area

## --
## veh_brand

## --
## veh_gas

## --
## veh_power

4.1.4 Date/Time Variables

Like the univariate plots, we facet on histograms of the years in the dates.

for (plot_varname in datetime_vars) {
  cat("--\n")
  cat(str_c(plot_varname, "\n"))

  plot_tbl <- data_tbl %>% filter(!are_na(!! plot_varname))

  explore_plot <- ggplot(plot_tbl) +
    geom_histogram(aes(x = !! sym(plot_varname)),
                   bins = hist_bins_count) +
    facet_wrap(facet_varname, scales = "free") +
    xlab(plot_varname) +
    ylab("Count") +
    scale_y_continuous(labels = label_comma()) +
    ggtitle(str_c(facet_varname, "-Faceted Histogram for Variable: ",
                  plot_varname))

  plot(explore_plot)
}

5 Custom Explorations

In this section you can add your own multivariate visualations such as boxplots and so on.

6 R Environment

sessioninfo::session_info()
## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.0.2 (2020-06-22)
##  os       Ubuntu 20.04.1 LTS          
##  system   x86_64, linux-gnu           
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       Etc/UTC                     
##  date     2021-02-04                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
##  package     * version date       lib source        
##  assertthat    0.2.1   2019-03-21 [1] RSPM (R 4.0.0)
##  backports     1.1.10  2020-09-15 [1] RSPM (R 4.0.2)
##  blob          1.2.1   2020-01-20 [1] RSPM (R 4.0.0)
##  bookdown      0.20    2020-06-23 [1] RSPM (R 4.0.2)
##  broom         0.7.1   2020-10-02 [1] RSPM (R 4.0.2)
##  cellranger    1.1.0   2016-07-27 [1] RSPM (R 4.0.0)
##  cli           2.1.0   2020-10-12 [1] RSPM (R 4.0.2)
##  colorspace    1.4-1   2019-03-18 [1] RSPM (R 4.0.0)
##  conflicted  * 1.0.4   2019-06-21 [1] RSPM (R 4.0.0)
##  cowplot     * 1.1.0   2020-09-08 [1] RSPM (R 4.0.2)
##  crayon        1.3.4   2017-09-16 [1] RSPM (R 4.0.0)
##  DBI           1.1.0   2019-12-15 [1] RSPM (R 4.0.0)
##  dbplyr        1.4.4   2020-05-27 [1] RSPM (R 4.0.0)
##  digest        0.6.25  2020-02-23 [1] RSPM (R 4.0.0)
##  dplyr       * 1.0.2   2020-08-18 [1] RSPM (R 4.0.2)
##  ellipsis      0.3.1   2020-05-15 [1] RSPM (R 4.0.0)
##  evaluate      0.14    2019-05-28 [1] RSPM (R 4.0.0)
##  fansi         0.4.1   2020-01-08 [1] RSPM (R 4.0.0)
##  farver        2.0.3   2020-01-16 [1] RSPM (R 4.0.0)
##  forcats     * 0.5.0   2020-03-01 [1] RSPM (R 4.0.0)
##  fs          * 1.5.0   2020-07-31 [1] RSPM (R 4.0.2)
##  generics      0.0.2   2018-11-29 [1] RSPM (R 4.0.0)
##  ggplot2     * 3.3.2   2020-06-19 [1] RSPM (R 4.0.1)
##  glue          1.4.2   2020-08-27 [1] RSPM (R 4.0.2)
##  gtable        0.3.0   2019-03-25 [1] RSPM (R 4.0.0)
##  haven         2.3.1   2020-06-01 [1] RSPM (R 4.0.2)
##  hms           0.5.3   2020-01-08 [1] RSPM (R 4.0.0)
##  htmltools     0.5.0   2020-06-16 [1] RSPM (R 4.0.1)
##  httr          1.4.2   2020-07-20 [1] RSPM (R 4.0.2)
##  jsonlite      1.7.1   2020-09-07 [1] RSPM (R 4.0.2)
##  knitr         1.30    2020-09-22 [1] RSPM (R 4.0.2)
##  labeling      0.3     2014-08-23 [1] RSPM (R 4.0.0)
##  lifecycle     0.2.0   2020-03-06 [1] RSPM (R 4.0.0)
##  lubridate   * 1.7.9   2020-06-08 [1] RSPM (R 4.0.2)
##  magrittr    * 1.5     2014-11-22 [1] RSPM (R 4.0.0)
##  memoise       1.1.0   2017-04-21 [1] RSPM (R 4.0.0)
##  modelr        0.1.8   2020-05-19 [1] RSPM (R 4.0.0)
##  munsell       0.5.0   2018-06-12 [1] RSPM (R 4.0.0)
##  pillar        1.4.6   2020-07-10 [1] RSPM (R 4.0.2)
##  pkgconfig     2.0.3   2019-09-22 [1] RSPM (R 4.0.0)
##  ps            1.4.0   2020-10-07 [1] RSPM (R 4.0.2)
##  purrr       * 0.3.4   2020-04-17 [1] RSPM (R 4.0.0)
##  R6            2.4.1   2019-11-12 [1] RSPM (R 4.0.0)
##  Rcpp          1.0.5   2020-07-06 [1] RSPM (R 4.0.2)
##  readr       * 1.4.0   2020-10-05 [1] RSPM (R 4.0.2)
##  readxl        1.3.1   2019-03-13 [1] RSPM (R 4.0.2)
##  reprex        0.3.0   2019-05-16 [1] RSPM (R 4.0.0)
##  rlang       * 0.4.8   2020-10-08 [1] RSPM (R 4.0.2)
##  rmarkdown     2.4     2020-09-30 [1] RSPM (R 4.0.2)
##  rmdformats    0.3.7   2020-03-11 [1] RSPM (R 4.0.0)
##  rstudioapi    0.11    2020-02-07 [1] RSPM (R 4.0.0)
##  rvest         0.3.6   2020-07-25 [1] RSPM (R 4.0.2)
##  scales      * 1.1.1   2020-05-11 [1] RSPM (R 4.0.0)
##  sessioninfo   1.1.1   2018-11-05 [1] RSPM (R 4.0.0)
##  snakecase   * 0.11.0  2019-05-25 [1] RSPM (R 4.0.0)
##  stringi       1.5.3   2020-09-09 [1] RSPM (R 4.0.2)
##  stringr     * 1.4.0   2019-02-10 [1] RSPM (R 4.0.0)
##  tibble      * 3.0.4   2020-10-12 [1] RSPM (R 4.0.2)
##  tidyr       * 1.1.2   2020-08-27 [1] RSPM (R 4.0.2)
##  tidyselect    1.1.0   2020-05-11 [1] RSPM (R 4.0.0)
##  tidyverse   * 1.3.0   2019-11-21 [1] RSPM (R 4.0.0)
##  utf8          1.1.4   2018-05-24 [1] RSPM (R 4.0.0)
##  vctrs       * 0.3.4   2020-08-29 [1] RSPM (R 4.0.2)
##  withr         2.3.0   2020-09-22 [1] RSPM (R 4.0.2)
##  xfun          0.18    2020-09-29 [1] RSPM (R 4.0.2)
##  xml2          1.3.2   2020-04-23 [1] RSPM (R 4.0.0)
##  yaml          2.2.1   2020-02-01 [1] RSPM (R 4.0.0)
## 
## [1] /usr/local/lib/R/site-library
## [2] /usr/local/lib/R/library